A solid cylinder and a hollow cylinder, both of the same mass and same external diameter are released from the same height at the same time on an inclined plane. Both roll down without slipping. Which one will reach the bottom first?

1. Both together only when the angle of inclination of the plane is ${45}^0$

2. Both together

3. Hollow cylinder

4. Solid cylinder

A body of mass \(M\) and radius \(R\) is rolling horizontally without slipping with speed \(v.\) It then rolls up a hill to a maximum height \(h.\) If \(h=\frac{5v^{2}}{6g},\) what is the moment of inertia of the body?
1. \(\frac{MR^{2}}{2}\)
2. \(\frac{2MR^{2}}{3}\)
3. \(\frac{3MR^{2}}{4}\)
4. \(\frac{2MR^{2}}{5}\)

A wheel of radius R rolls on the ground with a uniform velocity v. The velocity of topmost point relative to the bottommost point is

1. v

2. 2v

3. v/2

4. zero

A sphere is rolling down a plane of inclination $\theta$ to the horizontal.  The acceleration of its centre down the plane is 

1. g sin $\theta$                   

2. less than g sin $\theta$

3. greater than g sin $\theta$

4. zero

A body rolls down an inclined plane without slipping. The fraction of total energy associated with its rotation will be

$1.<mspace\; width="1em"></mspace>{\mathrm{K}}^2+<mspace\; width="1em"></mspace>{\mathrm{R}}^2$
$2.<mspace\; width="1em"></mspace>\frac{{\mathrm{K}}^2}{{\mathrm{R}}^2}$
$3.<mspace\; width="1em"></mspace>\frac{{\mathrm{K}}^2}{{\mathrm{K}}^2+<mspace\; width="1em"></mspace>{\mathrm{R}}^2}$
$4.<mspace\; width="1em"></mspace>\frac{{\mathrm{R}}^2}{{\mathrm{K}}^2+<mspace\; width="1em"></mspace>{\mathrm{R}}^2}$

Where k is radius of gyration of the body about an axis passing through centre of mass and R is the radius of the body.